AE419 Homework 3 Due 3/31/23 Problem 1: Stability and Control of a Boeing 747 Dr Arielle Hoomin-Person has accepted a temporary role as Contract Aerospace Engineer at Argon National Lab, where research scientists are studying aircraft emissions and new sustainable designs. Their current task is to reverse-engineer the early Boeing 747 from a stability and control perspective so that they can study next-generation replacements for aircraft of this scale and configuration. They have access to the NASA report titled "The Simulation of a Jumbo Jet Transport Aircraft. Volume 2: Modeling Data (found here). They decide to take part of the data they need from the report and approximate the rest from their experience with aerodynamics. Follow along as they reconstruct the stability diagrams of the Boeing 747-100. 12-7.2 -36-1.2- 32 2 CAMBERED KRUEGER FLAPS LOW SPEED AILERON KRUEGER FLAPS 21'4" 4 FLIGHT SPOILERS OUTBD FLAPS -FLAP TRACK FAIRING HIGH SPEED AILERON -FLIGHT SPOILER INBD FLAPS GROUND SPOILER -83-11.5"- 25 MAC 99'2' 231'4' -225-2 L14:7" 102 G OUTBOARD ELEVATOR INBOARD ELEVATOP 720 38'5" 113-1 UPPER TRUDDER 322 LOWER RUDDER GROUND LINE The following data is taken from the report, whether print or diagram: Value (English Units) Value (SI Units) 5500 sq ft 511 sq m 8.324 m 59.64 m 16.56 m Item Wing Area Wing MAC 27.31 ft Wing Span 195.68 ft Wing Root 54 ft 4 in Wing Tip 13 ft 4 in Tail Span Tail Root 72 ft 9 in 32 ft 4 in Tail Tip 8 ft 1 in Distance between Tail AC 102 ft and Wing AC Fuselage length 225 ft 2 in Fuselage width Max Takeoff Weight 21 ft 4 in 710,000 lbf 4.064 m 22.1742 m 9.855 m 2.4638 m 31.09 m 68.63 m 6.5024 m 322050 kg 31.75 m 31.625 m x-location of Wing AC x-location of CG (average of fwd and aft limits) Stabilizer trim deflection limits CMO at zero angle of attack CLO at zero angle of attack 104 ft 2 in 103 ft 9 in +3 deg, -12 deg The entire horizontal stabilizer is moving 0.14 0 You can make the following assumptions about flight conditions and aerodynamic characteristics: Altitude: 36089 ft (11000 m) Mach = 0.9 q=1pv Mach effects on CL: C{L,M=0} = C{L,M} 1 M - 2 Wing/Tail Lift curve slope (in 1/rad) depends on aspect ratio as CLawing 1+ AR Approximate as derived from far-field corrections in lifting line theory is de da : de CLaw = 2 da ARW To calculate Clawb" 2 (width fuse (width fuse kwb = 1 + 0.025 - 0.25 bwing bwing CLaw = CLakwb nt = 0.9 Assume that the fuselage has no effect on lift-curve slope Assume Xacwb Xacwing CLrequired atrim CLatot Dr. Hoomin-Person's workflow goes something like this (MIND YOUR UNITS!): a) Find the tail area, and consequently the tail volume coefficient. Xcg) Sref MACwing Stail (xactail VH = de b) Calculate the downwash effect da lift curve slope. using far-field corrections in lifting line theory and wing c) At the current CG location, find Ma: CMacg = CLawbw - nt VHC Latai (1 - de) d) Find the total lift curve slope of the airplane (1/rad or 1/deg, just stay consistent) Chatot = Clawb + nt (1 - de) Catal (Stall) da Sref e) From C and CLatot calculate CMacg SM = - CLatot = Xcg + SM (MACwing) f) Find the required CL at Mach 0.9 assuming SLUF and max takeoff weight. Transform the required lift coefficient to Mach 0, as that's where we're performing our stability analysis. g) Find a trimin degrees. h) Plot CM,total V/S CL over the AOA range [-3: 14] for stabilizer deflection at upper limit, at lower limit, and when stabilizer = 0. Provide your python or excel code used to generate the plot in part h) for full credit. Do not hand-draw the plot. CL(a) = CLatot de C() = + a - nt VHC Latall (1 Sstabilizer da. i) From the graph, report an estimate of the stabilizer trim deflection in degrees that would be needed to attain trim at the required CL. corrected for Mach effects If you're unsure about the value of that CL, use 0.4. Is the deflection positive or negative? Which direction is the tail producing lift in? j) Qualitatively explain (in two sentences maximum) what would happen to the graph when the CG moves. One sentence describing the slope, and another describing the y-intercepts. SR